(1) Field of the Invention
The present invention relates to a graphic display apparatus, and more particularly to a graphic display apparatus for subsequently reconstructing the desired rotated state of a displayed three-dimensional object after the operator has made rotative actions to rotate the displayed three-dimensional object.
(2) Description of the Related Art
It has heretofore been customary to display three-dimensional objects on two-dimensional graphic display apparatus. It has also been the usual practice to rotate a three-dimensional object on a two-dimensional display apparatus for the operator to observe the structural arrangement of the object. Such a displayed three-dimensional object can be rotated as desired by the operator using buttons that are provided for rotating displayed objects on the graphic display apparatus.
Generally, the operator of a computer rotates a three-dimensional figure displayed on a graphic display apparatus controlled by the computer by giving three Euler's angles to the computer. The initial state of a three-dimensional figure before it is rotated and the rotated state of the three-dimensional figure can be defined uniquely using Euler's angles. However, the operator usually finds it difficult to intuitively find Euler's angles for transforming a displayed three-dimensional figure from its initial state before being rotated to a desired rotated state. It is known that rotations about the three axes of the rectangular Cartesian coordinate system are recognizable most easily by human beings.
There are more than one sequence of rotative actions available for the operator to achieve the desired rotated state of a displayed three-dimensional figure from its initial state through rotations about the three axes of the rectangular Cartesian coordinate system. Specifically, the operator may achieve the desired rotated state of a displayed three-dimensional figure byrotating the figure about the X-, Y-, Z-axes successively in a sequence of rotative actions, e.g., first about the X-axis, then about the Y-axis, and finally about the Z-axis. Alternatively, the operator may rotate the figure about these axes successively in any of other sequences of rotative actions. Further alternatively, the operator may rotate the figure a plurality of times about each of these axes in any of available sequences of rotative actions. The operator can achieve the desired rotated state of the displayed three-dimensional figure no matter which sequence of rotative actions he may follow for rotating the figure about the axes.
To reconstruct a three-dimensional figure in the previously achieved rotated state again from the initial state, it is necessary to record the previously effected rotations, i.e., the axes and the rotational angles in their proper sequences, and carry out the recorded rotations again. Such a process is usually very complex to perform. The complexities of the process manifest themselves particularly when the three-dimensional figure is displayed on a graphic display apparatus and rotated to varythe displayed figure, for it is the general practice for the operator to repeat trial-and-error efforts to rotate a displayed three-dimensional figure a plurality of times while confirming the rotated figure on the graphic display apparatus until the displayed figure reaches the desired rotated state from its initial state.
Recent graphic display apparatus or graphic display software capable of rotating a three-dimensional object and displaying the rotated three-dimensional object often employ a mouse to control the rotation of the three-dimensional object comparatively easily.
With the conventional graphic display apparatus, however, more than one sequence of rotational operations are available for the operator to achieve the desired rotated state of a displayed three-dimensional figure from its initial state, as described above. Rotational angles about the axes from the initial state of the three-dimensional figure are not displayed as they are insignificant in the rotating procedure. The operator repeats rotations of a displayed three-dimensional figure on a graphic display apparatus until it reaches a desired rotated state, then turns off the graphic display apparatus, and thereafter turns on the graphic display apparatus again and tries to reconstruct the rotated three-dimensional figure. In such a case, however, the operator finds it difficult to reconstruct the rotated three-dimensional figure on the graphic display apparatus.